Summary
Highlights
Vectors are quantities that require both magnitude and direction, like velocity, displacement, and acceleration. Scalars, such as temperature, only require magnitude. Vectors are represented by an arrowhead line where the length signifies magnitude and the arrow indicates direction. The head and tail are important parts of a vector.
When vectors are in the same direction, they can be directly added. If in opposite directions, they are subtracted. For vectors in different directions, the graphical (tail-to-head) method involves drawing vectors to scale and connecting the initial tail to the final head to find the resultant vector. The analytical (component) method involves breaking down vectors into X and Y components. The Pythagorean theorem is used to find the resultant vector's magnitude if the vectors are perpendicular, and the tangent function is used to find its direction.
All physical quantities are measured relative to a reference frame. For example, measurements on Earth are typically taken with the Earth as the resting reference frame. The perception of an object's speed can differ significantly based on the chosen reference frame, as illustrated by the example of a person walking inside a moving train.
Distance is a scalar quantity, representing the total path traveled. Displacement is a vector quantity, representing the straight-line distance and direction from the starting point to the end point. Both are measured in meters (SI unit).
Velocity is the rate of change of displacement (a vector), while speed is the rate of change of distance (a scalar). Instantaneous velocity is the velocity at a specific moment. Acceleration is the rate of change of velocity (a vector). Positive acceleration means speeding up, and negative acceleration (deceleration) means slowing down. The units for velocity are meters per second, and for acceleration, meters per square second.
Understanding graphs is crucial in physics. A position-time graph's slope represents velocity. A velocity-time graph's slope represents acceleration. Linear plots on these graphs indicate constant velocity or acceleration. The y-intercept and slope of a linear plot relate to physical quantities and can be determined from the linear equation displayed on a graph.
Problems with constant acceleration are called kinematics problems. These involve relationships between displacement, velocity, acceleration, and time. Specific kinematic equations are used to solve for unknown variables, such as final velocity or displacement, given initial conditions like initial velocity, acceleration, and time. The choice of equation depends on the available information.
Free-fall motion refers to objects moving solely under the influence of gravity, assuming no other disturbances like air resistance. In this case, the acceleration is constant and equals the acceleration due to gravity (g), approximately -9.80 m/s^2 in the y-direction. Key aspects include: initial velocity being zero if an object is 'dropped', velocity increasing linearly, and displacement increasing parabolically. All objects, regardless of mass or size, fall with the same acceleration in a vacuum.
Non-free-fall motion occurs when air resistance or other disturbances affect the falling object. As an object falls, air resistance builds up, opposing the motion. Eventually, the upward air resistance force can balance the downward gravitational force, leading to zero net acceleration. At this point, the object reaches a constant velocity called terminal velocity. Skydiving is an example of non-free-fall motion.